#### Answer

$\dfrac{v^{6}\sqrt[]{v}}{7}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[]{\dfrac{v^{13}}{49}}
,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers.
$\bf{\text{Solution Details:}}$
Expressing the radicand of the expression above with a factor that is a perfect power of the index and then extracting the root of that factor results to
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{v^{12}}{49}\cdot v}
\\\\=
\sqrt[]{\left( \dfrac{v^{6}}{7} \right)^2\cdot v}
\\\\=
\dfrac{v^{6}}{7}\sqrt[]{v}
\\\\=
\dfrac{v^{6}\sqrt[]{v}}{7}
.\end{array}